Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
9001	20^42973-5583	55910	Enzo Doria	03/2013
9002	4*10^55906+21	55907	Robert Price	08/2016
9003	2^185713-111	55906	Lelio R Paula	03/2011
9004	13^50174+88	55891	Lelio R Paula	01/2013
9005	14569^6846+6846^14569	55879	Hans Havermann	08/2016
9006	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9007	3^117087-80	55865	Lelio R Paula	10/2012
9008	(7*10^55851-43)/9	55851	Robert Price	10/2014
9009	2^185519-169	55847	Lelio R Paula	03/2011
9010	7^66074+10	55840	Lelio R Paula	10/2012
9011	(19*10^55833-49)/3	55834	Robert Price	02/2017
9012	(2*10^55834-59)/3	55834	Robert Price	05/2017
9013	2^185463-4237	55830	Yves Minet	08/2018
9014	12^51732+5	55829	Lelio R Paula	01/2013
9015	3*2^185429+7	55821	Lelio R Paula	03/2014
9016	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
9017	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
9018	14427^7396+7396^14427	55819	Hans Havermann	08/2016
9019	10^55811+21	55812	Robert Price	01/2011
9020	10^55811-74103	55811	Patrick De Geest	12/2012
9021	11^53591-1530	55810	Enzo Doria	11/2012
9022	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
9023	2^185355-2145	55798	Lelio R Paula	03/2011
9024	14531^6912+6912^14531	55794	Hans Havermann	07/2016
9025	2^185327-1615	55789	Lelio R Paula	03/2011
9026	2^185280-12779	55775	Enzo Doria	10/2012
9027	15504^3955+3955^15504	55771	Hans Havermann	07/2016
9028	(2*10^55762-59)/3	55762	Robert Price	05/2017
9029	5^79770-44	55757	Lelio R Paula	10/2012
9030	18^44416-85	55755	Lelio R Paula	02/2013
9031	2^185208-459995	55754	Enzo Doria	06/2015
9032	2^185200+1185	55751	Lelio R Paula	03/2011
9033	(536*10^55748-23)/9	55750	Robert Price	11/2017
9034	7^65964+6^(65964-1)	55747	Robert Price	03/2016
9035	2^185151-237157	55737	Gary Barnes	09/2009
9036	110017^11055-102	55734	Enzo Doria	07/2012
9037	14754^5987+5987^14754	55729	Hans Havermann	07/2016
9038	12591^13592-13592^12591	55729	Norbert Schneider	07/2018
9039	40090!3-9	55711	Robert Price	09/2014
9040	9*10^55707+89	55708	Robert Price	11/2016
9041	2^185023-2257	55698	Yves Minet	06/2009
9042	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
9043	2^185006-93	55693	Lelio R Paula	03/2011
9044	2^185003-2515	55692	Yves Minet	07/2014
9045	2^184992-78557	55689	Jorge Menendez	02/2018
9046	3*10^55679+37	55680	Robert Price	10/2017
9047	6^71524-19	55657	Lelio R Paula	10/2012
9048	2^184872-2195	55653	Yves Minet	08/2013
9049	507^20572+20572^507	55648	Norbert Schneider	06/2016
9050	(86*10^55645-311)/9	55646	Robert Price	10/2017
9051	134^26151-133	55626	Norbert Schneider	03/2015
9052	15340^4221+4221^15340	55614	Hans Havermann	07/2016
9053	27743!2+2	55612	Robert Price	01/2013
9054	20^42744+81	55612	Lelio R Paula	02/2013
9055	14609^6406+6406^14609	55611	Hans Havermann	07/2016
9056	2^184724-112883	55608	Enzo Doria	06/2014
9057	13507^13074+13074^13507	55601	Hans Havermann	07/2016
9058	2^184689+129	55597	Lelio R Paula	03/2011
9059	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
9060	(22*10^55592-19)/3	55593	Robert Price	02/2017
9061	Phi(59984,89)	55582	Enzo Doria	05/2012
9062	11^53368+16	55578	Lelio R Paula	01/2013
9063	20^42717-1923	55577	Enzo Doria	03/2013
9064	117^26870+26870^117	55573	Serge Batalov	05/2014
9065	12^51488+55	55565	Lelio R Paula	01/2013
9066	(44*10^55558-17)/9	55559	Robert Price	06/2015
9067	(2*10^55559-23)/3	55559	Robert Price	09/2017
9068	10^55555+32857	55556	Patrick De Geest	06/2010
9069	10^55555-136721	55555	Patrick De Geest	06/2010
9070	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
9071	20^42696-2043	55549	Enzo Doria	03/2013
9072	(35*10^55547-737)/9	55548	Robert Price	11/2017
9073	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
9074	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
9075	5003^15013-160	55537	Enzo Doria	07/2012
9076	39^34896-2	55522	Lelio R Paula	08/2013
9077	(6^71345-61)/5	55517	Lelio R Paula	05/2014
9078	2^184407-3019	55513	Yves Minet	10/2014
9079	(43*10^55512-61)/9	55513	Robert Price	06/2015
9080	20^42667-843	55512	Enzo Doria	03/2013
9081	133^26134-132	55505	Norbert Schneider	03/2015
9082	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
9083	9*7^65667-4	55497	Lelio R Paula	09/2014
9084	2^184342-173	55493	Lelio R Paula	03/2011
9085	15^47182+92	55491	Lelio R Paula	02/2013
9086	5^79378+6	55483	Lelio R Paula	10/2012
9087	581^20068+20068^581	55472	Norbert Schneider	06/2016
9088	(2^184232+1)/257	55457	Donovan Johnson	03/2005
9089	18^44177-1415	55455	Enzo Doria	03/2013
9090	2^184203-2797867	55451	Enzo Doria	04/2016
9091	2^184189+17	55447	Lelio R Paula	03/2011
9092	2^184183+26123	55445	Yves Minet	01/2010
9093	Phi(77077,10)	55441	Ray Chandler	05/2009
9094	2^184141-113251	55432	Enzo Doria	07/2014
9095	2^184093-504613	55418	Gary Barnes	09/2009
9096	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
9097	2^184044-111269	55403	Enzo Doria	05/2014
9098	14051^8766+8766^14051	55401	Hans Havermann	07/2016
9099	98^27819+27819^98	55394	Serge Batalov	05/2014
9100	(178*10^55390-7)/9	55392	Robert Price	08/2017
9101	58046^9+9^58046	55390	Andrey Kulsha	02/2004
9102	7^65536+2*59232-2	55385	Jiahao He	07/2017
9103	2^183980+75241	55384	Enzo Doria	04/2016
9104	10^55372+37	55373	Robert Price	01/2011
9105	10^55372-49967	55372	Patrick De Geest	12/2012
9106	(13*10^55367+17)/3	55368	Robert Price	06/2015
9107	2*6^71150+7	55366	Lelio R Paula	09/2014
9108	19^43296-62	55365	Lelio R Paula	02/2013
9109	19^43295+10	55364	Lelio R Paula	02/2013
9110	(29*10^55362-11)/9	55363	Robert Price	04/2015
9111	(37*10^55359+53)/9	55360	Robert Price	05/2015
9112	19^43283+72	55349	Lelio R Paula	02/2013
9113	2^183800-65	55330	Lelio R Paula	03/2011
9114	21001^12801-110	55329	Enzo Doria	07/2012
9115	33^36433-32^36433	55325	Robert Price	04/2012
9116	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
9117	9^57952+8^(57952-1)	55301	Robert Price	03/2016
9118	14872^5229+5229^14872	55301	Hans Havermann	08/2016
9119	61^30972-2	55296	Lelio R Paula	08/2013
9120	2^183671-112537	55291	Enzo Doria	06/2014
9121	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
9122	3^115873+56	55286	Lelio R Paula	10/2012
9123	13^49629-84	55284	Lelio R Paula	01/2013
9124	2^183632-5	55279	Henri Lifchitz	08/2005
9125	13981^8988+8988^13981	55277	Hans Havermann	07/2016
9126	10688^13719-13719^10688	55273	Norbert Schneider	09/2018
9127	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
9128	2^183576+171	55262	Lelio R Paula	03/2011
9129	13^49604+82	55257	Lelio R Paula	01/2013
9130	(11*10^55254+1)/3	55255	Erik Branger	03/2014
9131	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
9132	3^115802-26	55252	Lelio R Paula	10/2012
9133	2^183534-3645	55250	Lelio R Paula	01/2011
9134	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
9135	5^79032-13766	55241	Enzo Doria	02/2013
9136	8*3^115759-7	55232	Lelio R Paula	03/2014
9137	6^70974-137	55229	Lelio R Paula	10/2012
9138	2^183466+524287	55229	Paul Underwood	08/2018
9139	2^183446-113073	55223	Enzo Doria	07/2014
9140	2^183441+577294575	55222	Lelio R Paula	03/2013
9141	5^79000-6	55219	Lelio R Paula	10/2012
9142	2^183413-901	55213	Yves Minet	01/2012
9143	19^43168-50	55202	Lelio R Paula	02/2013
9144	2^183340+19683	55191	Lelio R Paula	02/2012
9145	6^70923+35	55189	Lelio R Paula	10/2012
9146	2^183317-4035	55184	Lelio R Paula	01/2011
9147	2^183284-15	55174	Lelio R Paula	03/2011
9148	2^183255+149	55166	Lelio R Paula	02/2011
9149	4*10^55165+87	55166	Robert Price	05/2016
9150	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
9151	2^183165-112333	55139	Enzo Doria	06/2014
9152	(109^27061-1)/108	55133	Richard Fischer	09/2017
9153	2^183142+855	55132	Lelio R Paula	01/2011
9154	(49*10^55129+383)/9	55130	Robert Price	04/2017
9155	2^183019+255255	55095	Lelio R Paula	01/2011
9156	(10^55084-19)/9	55084	Robert Price	10/2017
9157	3*10^55077+7	55078	Erik Branger	11/2013
9158	(62*10^55075-71)/9	55076	Robert Price	09/2015
9159	27499!2-32	55070	Robert Price	10/2015
9160	15307^3958+3958^15307	55067	Hans Havermann	08/2016
9161	70^29836-69	55051	Norbert Schneider	10/2012
9162	18^43854-83	55049	Lelio R Paula	02/2013
9163	7^65126+58	55038	Lelio R Paula	10/2012
9164	2^182827-1615	55037	Lelio R Paula	11/2009
9165	7*10^55030-9	55031	Dmitry Domanov	11/2010
9166	9027^13912-13912^9027	55030	Norbert Schneider	08/2018
9167	2^182768-4055	55019	Yves Minet	02/2018
9168	6^70702+23	55017	Lelio R Paula	10/2012
9169	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
9170	2^182743-1615	55012	Lelio R Paula	11/2009
9171	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
9172	3^115280-9568	55003	Enzo Doria	02/2013
9173	2^182656-12849	54985	Enzo Doria	10/2012
9174	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
9175	9*19^42995+16	54981	Curtis Bright	05/2015
9176	2^182627+28425	54977	Lelio R Paula	11/2009
9177	2^182597-113053	54968	Enzo Doria	07/2014
9178	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
9179	2^182581-1975	54963	Yves Minet	09/2012
9180	(2*10^54960-179)/3	54960	Robert Price	11/2017
9181	27449!!-16	54959	Robert Price	06/2015
9182	(22*10^54958-73)/3	54959	Robert Price	09/2017
9183	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
9184	2^182565+107	54958	Lelio R Paula	11/2009
9185	2^182560+2053	54957	Lelio R Paula	12/2010
9186	2^182451-182451	54924	Henri Lifchitz	10/2004
9187	2^182444+81	54922	Henri Lifchitz	10/2005
9188	2^182433+74105	54918	Enzo Doria	04/2016
9189	20^42206-5243	54912	Enzo Doria	03/2013
9190	2^182394+85	54907	Lelio R Paula	02/2011
9191	2^182374-112287	54901	Enzo Doria	06/2014
9193	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
9192	10188^13697-13697^10188	54899	Norbert Schneider	09/2018
9194	2^182363-113167	54897	Enzo Doria	07/2014
9195	2^182359-112221	54896	Enzo Doria	06/2014
9196	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
9197	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
9198	18^43698-5	54853	Lelio R Paula	02/2013
9199	2^182209-1893	54851	Yves Minet	09/2012
9200	2^182194-3443	54846	Yves Minet	12/2016
9201	15023^4468+4468^15023	54836	Hans Havermann	08/2016
9202	2^182135+90143	54829	Yves Minet	10/2010
9203	2^182119+74333	54824	Enzo Doria	04/2016
9204	14289^6860+6860^14289	54818	Hans Havermann	08/2016
9205	3^114892-114892^3	54818	Norbert Schneider	03/2017
9206	2^182070-47355	54809	Lelio R Paula	01/2011
9207	3^114869+76	54807	Lelio R Paula	10/2012
9208	8^60681-60681^8	54801	Norbert Schneider	12/2016
9209	1897^16710+16710^1897	54777	Serge Batalov	05/2014
9210	Phi(61868,59)	54776	Enzo Doria	04/2012
9211	113^26679+2	54775	Lelio R Paula	05/2013
9212	3^114789-74	54769	Lelio R Paula	10/2012
9213	15^46567+98	54768	Lelio R Paula	02/2013
9214	(2*10^54767-71)/3	54767	Robert Price	01/2017
9215	(298*10^54765-7)/3	54767	Robert Price	06/2017
9216	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
9218	2^181913+29	54762	Henri Lifchitz	06/2005
9217	(31*10^54761-121)/9	54762	Robert Price	06/2016
9219	2^181887+189	54754	Lelio R Paula	02/2011
9220	2^181874+181874^2-1	54750	Robert Price	04/2014
9221	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
9222	5^78314-92	54740	Lelio R Paula	10/2012
9223	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
9224	15^46531+74	54725	Lelio R Paula	02/2013
9225	277^22400-348	54712	Enzo Doria	07/2012
9226	6^70302+101	54706	Lelio R Paula	10/2012
9227	3^114622-10408	54689	Enzo Doria	02/2013
9229	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
9228	2^181669-1551	54688	Yves Minet	08/2012
9230	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
9231	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
9232	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
9233	13^49073+46	54665	Lelio R Paula	01/2013
9234	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
9236	20^42000+73	54644	Lelio R Paula	02/2013
9235	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
9237	33*10^54634+7	54636	Robert Price	07/2016
9238	20^41988+61	54628	Lelio R Paula	01/2013
9239	20^41988-8123	54628	Enzo Doria	03/2013
9241	2^181420+21181	54613	Yves Minet	03/2011
9240	9854^13675-13675^9854	54613	Norbert Schneider	08/2018
9242	(19*10^54608+161)/9	54609	Robert Price	07/2016
9243	19^42696-24	54598	Lelio R Paula	02/2013
9244	(44*10^54596-503)/9	54597	Robert Price	10/2017
9245	(74*10^54583+61)/9	54584	Robert Price	10/2015
9246	2^181316-94395	54582	Lelio R Paula	09/2011
9247	14751^5006+5006^14751	54572	Hans Havermann	08/2016
9248	14^47609+39	54567	Lelio R Paula	02/2013
9249	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
9250	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017

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Probable Primes Top 10000

(225451 PRPs in the top)